Several authors [1]}, [2]} used merit-weighted exposurealso called “equity of attention” [2]}, “disparate treatment” [4]} \({v}^{\prime }_j(P) = {v}(P)/\overline{\mu }_j\)  where \(\overline{\mu }_j=\frac{1}{n}\sum _{i=1}^n\mu _{ij}\)  is the average value of item \(j\)  across users, rather than the exposure itself. We keep the non-weighted exposure to simplify the exposition, but our method straightforwardly applies to merit-weighted exposure. Note however that the sum of weighted exposures is not constant, so using (REF ) with merit-weighted exposures is not strictly equivalent to minimizing the Gini index.
